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Modified Korteweg-de Vries hierarchy with hodograph transformation: Camassa-Holm and Harry-Dym hierarchies
(Elsevier B.V., 2001-03-15)
In this paper, we present relations between Camassa-Holm (CH), Harry-Dym (HD) and modified Korteweg-de Vries (mKdV) hierarchies, which are given by the hodograph type transformation. (C) 2001 IMACS. Published by Elsevier ...
The higher grading structure of the WKI hierarchy and the two-component short pulse equation
(Springer, 2012-08-01)
A higher grading affine algebraic construction of integrable hierarchies, containing the Wadati-Konno-Ichikawa (WKI) hierarchy as a particular case, is proposed. We show that a two-component generalization of the Schafer-Wayne ...
Gauge Miura and Bäcklund transformations for generalized An-KdV hierarchies
(2021-10-29)
The construction of Miura and Bäcklund transformations for An mKdV and KdV hierarchies are presented in terms of gauge transformations acting upon the zero curvature representation. As in thewell knownsl(2) case, we derive ...
REDUCTION OF TODA LATTICE HIERARCHY TO GENERALIZED KDV HIERARCHIES AND THE 2-MATRIX MODEL
(World Scientific Publ Co Pte Ltd, 1995-07-10)
Toda lattice hierarchy and the associated matrix formulation of the 2M-boson KP hierarchies provide a framework for the Drinfeld-Sokolov reduction scheme realized through Hamiltonian action within the second KP Poisson ...
Defects in the supersymmetric mKdV hierarchy via Bäcklund transformations
(2018-01-01)
The integrability of the N= 1 supersymmetric modified Korteweg de-Vries (smKdV) hierarchy in the presence of defects is investigated through the construction of its super Bäcklund transformation. The construction of such ...
Generalized Bäcklund transformations for affine Toda hierarchies
(2021-02-12)
The construction of generalized Bäcklund transformation for the An affine Toda hierarchy is proposed in terms of gauge transformation acting on the zero curvature representation. Such construction is based upon the graded ...
Construction of type-II Bäcklund transformation for the mKdV hierarchy
(2015-09-14)
From an algebraic construction of the mKdV hierarchy we observe that the space component of the Lax operator plays the role of a universal algebraic object. This fact induces the universality of a gauge transformation that ...
Toda lattice field theories, discrete W algebras, Toda lattice hierarchies and quantum groups
(1996-10-31)
In analogy with the Liouville case we study the sl3 Toda theory on the lattice and define the relevant quadratic algebra and out of it we recover the discrete W3 algebra. We define an integrable system with respect to the ...
Normal numbers and the Borel hierarchy
(Polish Academy of Sciences. Institute of Mathematics, 2014-02)
We show that the set of absolutely normal numbers is Π03-complete in the Borel hierarchy of subsets of real numbers. Similarly, the set of absolutely normal numbers is Π03-complete in the effective Borel hierarchy.
Loop algebra and visaoro symmetries of integrable hierarchies of KP type
(2001-01-01)
We propose a systematic treatment of symmetries of KP integrable systems, including constrained (reduced) KP models cKP R, M (generalized AKNS hierarchies), and their multi component (matrix) generalizations. Any cKP R, M ...